Xmod-SIS.RmdThe SIS model, as it is now called, is a simple compartmental model, first introduced by Ross. It is included in `ramp.xde`` as a base model.
\(r\) is the rate infections clear
\(b\) is the fraction of bites by infective mosquitoes that transmit parasites and cause an infection.
\(c\) is the fraction of bites on an infectious human that would infect a mosquito.
The model defined herein is defined in two parts. To model exposure and infection (i.e. the conversion of eir into foi), we assume that the fraction of infective bites that cause an infection is \(b\). The dynamics are given by:
\[ \frac{dI}{dt} = h (H-I)-rI \]
Net Infectiousness
True prevalence is:
\[x = \frac{X}{H}.\]
In our implementation, net infectiousness (NI) is linearly proportional to prevalence:
\[c x.\]
Human Transmitting Capacity
After exposure, a human would remain infected for \(1/r\) days, transmitting with probability \(c\) so:
\[c/r\]
Exposure and Infection
In this model family, there is no immunity. The model assumes that a constant fraction of all infectious bites, \(b\), cause an infection.